Infinitesimal Extensions of P^1 and their Hilbert Schemes

Details Infinitesimal Extensions of P^1 and their Hilbert Schemes Infinitesimal Extensions of P^1 and their Hilbert Schemes

2001-10-08

arxiv.org/abs/math/0110083v1

Mathematics

Algebraic Geometry

22 pages

Scientific paper

In order to calculate the multiplicity of an isolated rational curve C in a local complete intersection variety X, i.e. the length of the Hilbert scheme of X at [C], it is important to study infinitesimal neighborhoods of the curve in X. This is equivalent to infinitesimal extensions of P^1 by locally free sheaves. In this paper we study infinitesimal extensions of P^1, determine their structure and obtain upper and lower bounds for the length of the local rings of their Hilbert schemes at [P^].

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